Skip to main content
PMC home page
Genetics logoLink to Genetics
. 1991 Nov;129(3):925–930. doi: 10.1093/genetics/129.3.925

Three-Locus Systems Impose Additional Constraints on Pairwise Disequilibria

W P Robinson 1, M A Asmussen 1, G Thomson 1
PMCID: PMC1204758  PMID: 1752428

Abstract

Combinations of allele frequencies and pairwise linkage disequilibrium terms, each of which is permissible at the two-locus level, may not always be permissible at the three-locus level. These additional constraints on the possible maximum and minimum values for the pairwise disequilibrium terms are formally determined and numerically analyzed. In some cases, the three-locus constraints on a pairwise disequilibrium (D) may be equivalent to the usual two-locus constraints, while in others, the positive or negative range may be restricted. This can result in situations where the allowable values of D are limited to only positive or only negative values up to the extreme case where there is only a single admissible value. No additional restrictions are placed on pairwise disequilibrium values when four loci are considered, other than those imposed by the three-way combinations containing the two loci of interest. A new measure of normalized pairwise linkage disequilibrium, allowing for the three-locus constraints, is defined and illustrated by an application to data from the human histocompatibility antigen (HLA) system. An analogous normalized three-way disequilibrium measure is also formulated.

Full Text

The Full Text of this article is available as a PDF (580.0 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. BENNETT J. H. On the theory of random mating. Ann Eugen. 1954 Mar;18(4):311–317. doi: 10.1111/j.1469-1809.1952.tb02522.x. [DOI] [PubMed] [Google Scholar]
  2. Hedrick P. W. Gametic disequilibrium measures: proceed with caution. Genetics. 1987 Oct;117(2):331–341. doi: 10.1093/genetics/117.2.331. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Hedrick P. W., Thomson G. A two-locus neutrality test: applications to humans, E. coli and lodgepole pine. Genetics. 1986 Jan;112(1):135–156. doi: 10.1093/genetics/112.1.135. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Hill W. G. Disequilibrium among several linked neutral genes in finite population 1. mean changes in disequilibrium. Theor Popul Biol. 1974 Jun;5(3):366–392. doi: 10.1016/0040-5809(74)90059-8. [DOI] [PubMed] [Google Scholar]
  5. Jennings H S. The Numerical Results of Diverse Systems of Breeding, with Respect to Two Pairs of Characters, Linked or Independent, with Special Relation to the Effects of Linkage. Genetics. 1917 Mar;2(2):97–154. doi: 10.1093/genetics/2.2.97. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Lewontin R C. The Interaction of Selection and Linkage. I. General Considerations; Heterotic Models. Genetics. 1964 Jan;49(1):49–67. doi: 10.1093/genetics/49.1.49. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Lewontin R. C. On measures of gametic disequilibrium. Genetics. 1988 Nov;120(3):849–852. doi: 10.1093/genetics/120.3.849. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Robbins R B. Applications of Mathematics to Breeding Problems II. Genetics. 1918 Jan;3(1):73–92. doi: 10.1093/genetics/3.1.73. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Robinson W. P., Cambon-Thomsen A., Borot N., Klitz W., Thomson G. Selection, hitchhiking and disequilibrium analysis at three linked loci with application to HLA data. Genetics. 1991 Nov;129(3):931–948. doi: 10.1093/genetics/129.3.931. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Schnabel A., Asmussen M. A. Definition and properties of disequilibria within nuclear-mitochondrial-chloroplast and other nuclear-dicytoplasmic systems. Genetics. 1989 Sep;123(1):199–215. doi: 10.1093/genetics/123.1.199. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Slatkin M. On treating the chromosome as the unit of selection. Genetics. 1972 Sep;72(1):157–168. doi: 10.1093/genetics/72.1.157. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Thomson G., Baur M. P. Third order linkage disequilibrium. Tissue Antigens. 1984 Oct;24(4):250–255. doi: 10.1111/j.1399-0039.1984.tb02134.x. [DOI] [PubMed] [Google Scholar]
  13. Thomson G., Klitz W. Disequilibrium pattern analysis. I. Theory. Genetics. 1987 Aug;116(4):623–632. doi: 10.1093/genetics/116.4.623. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Thomson G. The effect of a selected locus on linked neutral loci. Genetics. 1977 Apr;85(4):753–788. doi: 10.1093/genetics/85.4.753. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Weir B. S., Hill W. G. Effect of mating structure on variation in linkage disequilibrium. Genetics. 1980 Jun;95(2):477–488. doi: 10.1093/genetics/95.2.477. [DOI] [PMC free article] [PubMed] [Google Scholar]

Articles from Genetics are provided here courtesy of Oxford University Press

RESOURCES